1 Answer
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Whenever damage reduction completely negates the damage from an attack, it also negates most special effects that accompany the attack, such as injury poison, a monk's stunning, and injury-based disease. Damage reduction does not negate touch attacks, energy damage dealt along with an attack, or energy drains. Nor does it affect poisons or diseases delivered by inhalation, ingestion, or contact.

This is a touch attack, so DR will not stop this, doubly so as there is no damage to stop/negate thus the entire attack is str loss, not damage.

Other situations

For other attacks it will depend on how the ability damage is delivered.

If the attack is a non-touch attack and deals damage to the target and also drains ability damage through (say) poison or disease then if the DR stops all the damage the poison and therefore ability drain is stopped.

If the attack is a non-damaging touch type attack (Such as the Shadow) then the ability damage isn't negated, the DR has no effect. Note this would also include spells such as Touch of Idiocy - DR is no protection against this.

This answer focuses too much on the fact that the example given is a touch attack. The question specifically wondered about ability damage, which this answer barely touches on.
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dlras2Feb 19 '13 at 14:32

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Good point; tidied it up to clarify for generic situations.
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RobFeb 19 '13 at 14:39

Ah, where are you getting the idea that touch attacks aren't subject to DR? It has nothing to do with if it's a touch attack or not; damage reduction only reduces slashing, piercing, and/or bludgeoning damage and never reduces energy damage, force damage, negative energy damage, ability damage, etc.
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Lord_GarethFeb 19 '13 at 16:55

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@Lord_Gareth The point being that if for example a sword does 2 damage + 1d8 Strength to a character with 3/-, the 1d8 Strength is negated by the DR.
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Cristol.GdMFeb 19 '13 at 17:30